Stability And Hopf Bifurcation Analysis Of Mammalian Circadian Rhythm Model With Time Delay

The circadian rhythm(?24h)exists in most organisms and controls its physiological processes.Once the circadian rhythm is abnormal,it will mean a series of diseases.It is now widely accepted that transcription and translation delays are ubiquitous in the generation of circadian rhythms.Therefore,it is very important to study the role of time delay in the circadian rhythm.However,so far,the influence of this time delay on the circadian rhythm is lacking both experimentally and theoretically.In the article we passed Construct a mathematical model with time delay to study the dynamic behavior of mammalian circadian rhythm.The main contents are as follows:The first chapter,First,we introduce the background and significance of the study of circadian rhythm.Secondly,the development of the model is briefly described.Finally,a new model is constructed by introducing time delay.In the second chapter,we study the dynamics of a five-dimensional mammal circadian rhythm model with two time delays.Firstly,the time-delay is used as a parameter to determine the conditions under which the oscillation occurs.Secondly,using the normative theory and the central flow theorem the system Hopf bifurcation property formula is derived.Finally,the correctness of the theoretical results is verified by numerical simulation.In the third chapter,we use the same method as the second chapter to study the dynamics of an eight-dimensional mammalian circadian rhythm model with two time delays.The purpose is to study the role and influence of time delay in the circadian rhythm.In addition,we also the influence of parameters on the dynamics of circadian rhythm is considered.The results of this paper show that the time delay is crucial for the oscillation of mammalian circadian rhythm.The time delay not only determines whether oscillation will occur,but also determines the period length of the oscillation.In addition,the parameter size is also the reason for the change in circadian rhythm oscillation.In the article we found that the parameter size will cause the change of the state of the circadian system.Within a certain range,the size of the parameter determines the length of the period.